Molecular Weight Distributions in Coupled Polymers UsingZ-Transform

Abstract

A study of end-to-end coupling reactions of bifunctional linear prepolymers of the Schulz–Flory type is presented by use of Z-transform. The application of Z-transform allows one to derive exact expressions for the change of molecular weight distributions in dependence of the progress of the coupling reaction. After coupling the distribution is also of Schulz–Flory type, however, it depends in a relatively complicated manner on the extent of reaction of the prepolymer and on the extent of the coupling reaction. Further expressions are derived for various dependencies including the influence of the extent of coupling on the average molecular weights, chain lengths, and polymolecularity. By implementation of the Mark–Houwink–Sakurada equation, a correlation between intrinsic viscosity and the progress of coupling reaction is shown.